At the moment, the manage_custom_field_page.php page checks the following to get access to the screen.
<pre>access_ensure_global_level( config_get( 'manage_custom_fields_threshold' ) );</pre>
This means that the user's main global role has to be at least manage_custom_fields_threshold in order to manage any custom field from any project.

The problem here is that you might want a global "viewer" account but "manager" project account to have access to the custom fields for the projects specifically being managed.

This can just be purely for editing the custom field, but doesn't have to be for linking custom fields to projects.